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Article ON A GENERALIZED α-ADMISSIBLE RATIONAL TYPE CONTRACTIVE MAPPING(Yokohama Publ, 2016) Erhan, Inci M.; Kir, MehmetRecently, many generalized contractive conditions which involve rational contractive inequalities have been introduced in the context of partially ordered metric spaces. In this paper, we aim to give a generalized rational contractive condition which involves some of these results without need of extra restrictions.Article Citation - WoS: 144Citation - Scopus: 156Uniqueness of Solution for Higher-Order Nonlinear Fractional Differential Equations With Multi-Point and Integral Boundary Conditions(Springer-verlag Italia Srl, 2021) Sevinik-Adiguzel, Rezan; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.This study is devoted to the development of alternative conditions for existence and uniqueness of nonlinear fractional differential equations of higher-order with integral and multi-point boundary conditions. It uses a novel approach of employing a fixed point theorem based on contractive iterates of the integral operator for the corresponding fixed point problem. We start with developing an existence-uniqueness theorem for self-mappings with contractive iterate in a b-metric-like space. Then, we obtain the unique solvability of the problem under suitable conditions by utilizing an appropriate b-metric-like space.Article Citation - WoS: 79Citation - Scopus: 82A Generalized Contraction Principle With Control Functions on Partial Metric Spaces(Pergamon-elsevier Science Ltd, 2012) Abdeljawad, Thabet; Karapinar, Erdal; Tas, KenanPartial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In this article, we prove a generalized contraction principle with control functions phi and psi on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 171Citation - Scopus: 191Coincidence Point Theorems on Metric Spaces via Simulation Functions(Elsevier Science Bv, 2015) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Concepcion; Martinez-Moreno, JuanDue to its possible applications, Fixed Point Theory has become one of the most useful branches of Nonlinear Analysis. In a very recent paper, Khojasteh et al. introduced the notion of simulation function in order to express different contractivity conditions in a unified way, and they obtained some fixed point results. In this paper, we slightly modify their notion of simulation function and we investigate the existence and uniqueness of coincidence points of two nonlinear operators using this kind of control functions. (C) 2014 Elsevier B.V. All rights reserved.Article Citation - WoS: 93Solution of Fractional Differential Equations Via Coupled Fixed Point(Texas State Univ, 2015) Afshari, Hojjat; Kalantari, Sabileh; Karapinar, ErdalIn this article, we investigate the existence and uniqueness of a solution for the fractional differential equation by introducing some new coupled fixed point theorems for the class of mixed monotone operators with perturbations in the context of partially ordered complete metric space.Article Citation - WoS: 13Citation - Scopus: 13Best Proximity Point Results in Dislocated Metric Spaces Via r-functions(Springer-verlag Italia Srl, 2018) Gholizadeh, Leila; Karapinar, ErdalIn this paper, we investigate the existence of best proximity of R-contractions in the frame of dislocated metric spaces. We also propose some conditions to guarantee the uniqueness of best proximity point for such contractions. We consider an illustrative example to support the given results. This result generalizes a number of recent results on the topic in the literature.Article Citation - Scopus: 76Fixed Points of Generalized Α-Admissible Contractions on B-Metric Spaces With an Application To Boundary Value Problems(Yokohama Publications, 2016) Aksoy,Ü.; Karapinar,E.; Erhan,I.M.A general class of α-admissible contractions defined via (b)-comparison functions on b-metric spaces is discussed. Existence and uniqueness of the fixed point for this class of contractions is studied. Some consequences are presented. The results are employed in the discussion of existence and uniqueness of solutions of first order boundary value problems for ordinary differential equations. © 2016.Article Citation - Scopus: 10Note on “modified Α-Ψ Mappings With Applications”(Chiang Mai University, 2015) Berzig,M.; Karapinar,E.In this short paper, we unexpectedly notice that the modified version of α-ψ-contractivemappings, suggested by Salimi et al. [Modified α-ψ-contractive mappings with applications, Fixed Point Theory and Applications 2013, 2013:151] is not a real generalization. © 2015 by the Mathematical Association of Thailand. All rights reserved.Article Citation - WoS: 16Citation - Scopus: 16Fixed Points of Weakly Compatible Mappings Satisfying Generalized Φ-Weak Contractions(Malaysian Mathematical Sciences Soc, 2015) Vetro, Calogero; Chauhan, Sunny; Karapinar, Erdal; Shatanawi, WasfiIn this paper, utilizing the notion of the common limit range property, we prove some new integral type common fixed point theorems for weakly compatible mappings satisfying a phi-weak contractive condition in metric spaces. Moreover, we extend our results to four finite families of self mappings, and furnish an illustrative example and an application to support our main theorem. Our results improve, extend, and generalize well-known results on the topic in the literature.Article Citation - WoS: 45Citation - Scopus: 45A Note on "some Results on Multi-Valued Weakly Jungck Mappings in b-metric Space"(versita, 2013) Bota, Monica-Felicia; Karapinar, ErdalThe proofs of Theorems 2.1, 2.2 and 2.3 from [Olatinwo M.O., Some results on multi-valued weakly jungck mappings in b-metric space, Cent. Eur. J. Math., 2008, 6(4), 610-621] base on faulty evaluations. We give here correct but weaker versions of these theorems.
